What do the following two equations represent? $-2x-3y = -5$ $4x+6y = 3$
Solution: Putting the first equation in $y = mx + b$ form gives: $-2x-3y = -5$ $-3y = 2x-5$ $y = -\dfrac{2}{3}x + \dfrac{5}{3}$ Putting the second equation in $y = mx + b$ form gives: $4x+6y = 3$ $6y = -4x+3$ $y = -\dfrac{2}{3}x + \dfrac{1}{2}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.